On the Equivalence of Weak- and Cyclic-Monotonicity
39 Pages Posted: 22 Jul 2019 Last revised: 5 Aug 2019
Date Written: August 3, 2019
We provide an approach to studying the equivalence of weak- and cyclic-monotonicity conditions in convex and non-convex domains with a finite set of outcomes. Using this approach, we establish the new equivalence results for gross-substitutes preferences and single-peaked preferences on posets. We also provide novel applications of the equivalence result to problems in mechanism design, spatial allocation, revealed preference theory, and producer choice theory.
Keywords: weak-monotonicity, cyclic-monotonicity, non-convex domain, mechanism design, spatial allocation, revealed preference theory, producer choice theory, algebraic topology, homology
JEL Classification: D11, D21, D82
Suggested Citation: Suggested Citation